Gauss’s Law

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Physics Electromagnetism Gauss’s Law

	Experimental tests of Gauss’s law and Coulomb’s law:
	Let us consider a positively charged metal ball at the end of a silk thread that is lowered through a small opening into an uncharged hollow conductor that is insulated from ground. The positively charged ball induces a negative charge on the inner wall of the hollow conductor leaving an equal positive charge on the outer wall. The presence of positive charge on the outer wall is indicated by the deflection of the needle of an electrometer. The ball is then lowered and allowed to touch the inner surface of the hollow conductor. Charge is transferred between the ball and the inner surface so that neither is charged after contact is made. The needle deflection remains unchanged while this happens, indicating that the charge on the outer surface is unaffected. When the ball is removed, the electrometer reading remains the same. Furthermore, the ball is found to be uncharged; this verifies that the charge was transferred between the ball and the inner surface of the hollow conductor. The overall effect is that the charge that was originally on the ball now appears on the hollow conductor. The fact that the deflection of the needle on the electrometer measuring the charge on the outer surface remained unchanged regardless of what was happening inside the hollow conductor indicates that the net charge on the system always resided on the outer surface of the conductor. If we now apply another positive charge to the metal ball and place it near the outside of the conductor, it is repelled by the conductor. This demonstrates that E ≠ 0 outside the conductor implying that the conductor carries a net charge. If the charged metal ball is now lowered into the interior of the charged hollow conductor, it exhibits no evidence of an electric force. This shows E = 0 inside the hollow conductor. The experiment verifies the predictions of Gauss’s law and therefore verifies Coulomb’s law.